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A high-order integral equation-based solver for the time-dependent Schrodinger equation [article]

Jason Kaye, Alex Barnett, Leslie Greengard
2020 arXiv   pre-print
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation.  ...  This has several advantages: it avoids the need for artificial boundary conditions, admits simple, inexpensive high-order implicit time marching schemes, and naturally includes time-dependent potentials  ...  The Flatiron Institute is a division of the Simons Foundation.  ... 
arXiv:2001.06113v1 fatcat:p2twwnphrvfb3kdzvbtovxfwkm

Massively parallel algorithms for computational nanoelectronics based on quantum molecular dynamics

Aiichiro Nakano, Priya Vashishta, Rajiv K. Kalia
1994 Computer Physics Communications  
The core components of the QMD algorithm are: (i) solution of the time-dependent Kohn-Sham or Schrödinger equations; and (ii) solution of the Poisson equation for the direct electron-electron interaction  ...  Efficient parallel algorithms for these components are the space-splitting Schrödinger solver and the dynamical-simulated-annealing Poisson solver.  ...  The computations were performed using the computing facilities in the Concurrent Computing Laboratory for Materials Simulations (CCLMS) at Louisiana State University.  ... 
doi:10.1016/0010-4655(94)90047-7 fatcat:vqsmoolp6bdkvkpcpu46xfznxe

Time-Domain Simulations of the Nonlinear Maxwell Equations Using Operator-Exponential Methods

Martin Pototschnig, Jens Niegemann, Lasha Tkeshelashvili, Kurt Busch
2009 IEEE Transactions on Antennas and Propagation  
In this paper, we propose a Krylov-subspace-based operator-exponential method for time-domain simulations of the Maxwell equations with general nonlinear polarizations.  ...  As an illustration, we compare the performance of our approach to certain well-known methods for the case of pulse self-steepening in a material with negative Kerr-nonlinearity.  ...  that make it very competitive as a high-order solver for the nonlinear Maxwell equations (see Section III).  ... 
doi:10.1109/tap.2008.2011181 fatcat:numuzdye4zgknd42owddld2fma

Efficient numerical integrator based on Fer expansion: Application to solid-state NMR experiments and to solve quantum Liouville equation and quantum Fokker-Planck equation

Eugene Stephane Mananga
The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation (TDSE) which  ...  First, we plan to develop an efficient numerical integrator based on Fer expansion for solid-state NMR simulation of experiments.  ...  INTRODUCTION The goal of the proposed research is to study a numerical integrator based on Fer expansion (Fer integrators of higher orders) in the integration of the time-dependent Schrodinger equation  ... 
doi:10.24297/jap.v13i4.6011 fatcat:pu6xtnyttrcuzn5krcrlgm6264

A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrödinger Equation with Discontinuous Potentials

Xin Wen
2009 Journal of Scientific Computing  
We develop a fourth order numerical method for the computation of multivalued physical observables (density, momentum, etc.) in the semiclassical limit of the one dimensional linear Schrödinger equation  ...  We achieve high order accuracy for our method by studying two issues.  ...  He thanks IPAM for the inspiring research environment and warm hospitality.  ... 
doi:10.1007/s10915-009-9326-9 fatcat:qwchvp5ygbconcoe44ubkp2htq

Fiend -- Finite Element Quantum Dynamics [article]

Janne Solanpää, Esa Räsänen
2019 arXiv   pre-print
We present Fiend - a simulation package for three-dimensional single-particle time-dependent Schrödinger equation for cylindrically symmetric systems.  ...  The underlying spatial discretization is based on the finite element method (FEM), and time-stepping is provided either via the generalized-α or Crank-Nicolson methods.  ...  This work was supported by the Alfred Kordelin foundation and the Academy of Finland (grant no. 304458). We also acknowledge CSC -the Finnish IT Center for Science -for computational resources.  ... 
arXiv:1812.05943v2 fatcat:2dlnkubyfzfm3c7geyh2hyxqqi

Using numerical methods from nonlocal optics to simulate the dynamics of N-body systems in alternative theories of gravity [article]

Tiago D. Ferreira, Nuno A. Silva, O. Bertolami, C. Gomes, A. Guerreiro
2019 arXiv   pre-print
Indeed, in this work we report the development of a solver for the HiLight simulations platform based on GPGPU supercomputing and the required adaptations for this solver to be used to test the impact  ...  Thus, the numerical solvers developed for studying light propagating under this model can be adapted to address these other phenomena.  ...  Funds through the Portuguese funding agency, FCT -Fundação para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-032257  ... 
arXiv:1909.08354v1 fatcat:jpk5jlpz4fdahixswq65634wwy

SCALAR: an AMR code to simulate axion-like dark matter models [article]

Mattia Mina, David F. Mota, Hans A. Winther
2020 arXiv   pre-print
We present a new code, SCALAR, based on the high-resolution hydrodynamics and N-body code RAMSES, to solve the Schr\"odinger equation on adaptive refined meshes.  ...  be used as a standalone solver for both linear and non-linear Schr\"odinger equations with any given external potential.  ...  Computations were performed on resources provided by UNINETT Sigma2 -the National Infrastructure for High Performance Computing and Data Storage in Norway.  ... 
arXiv:1906.12160v2 fatcat:pex7s3e52jfu3nlfevooiwtnqe

A non-linear variational principle for the self-consistent solution of Poisson's equation and a transport equation in the local density approximation

H. Carrillo-Nunez, Wim Magnus, F. M. Peeters
2010 2010 International Conference on Simulation of Semiconductor Processes and Devices  
In order to simplify the numerical investigation of carrier transport in nanodevices without jeopardizing the rigor of a full quantum mechanical treatment, we have exploited an existing variational principle  ...  to solve self-consistently Poisson's equation and Schrödinger's equation as well as an appropriate transport equation within the scope of the generalized local density approximation (GLDA).  ...  ACKNOWLEDGMENT This work was supported by Flemish Science Fundation (FWO-VI) and the Interuniversity Attraction Poles, Belgium State, Belgium Science Policy, and imec.  ... 
doi:10.1109/sispad.2010.5604537 fatcat:u7s6nbyysfdbfoqtyccfwcs5gy

Quantum interference of high-order harmonics from mixed gases

A. González-Fernández, P. Velarde
2016 Physical Review A  
At higher-order harmonics, where there are no experimental data, comparison is with a Schrodinger solver. This work has been published at PHYSICAL REVIEW A 94, 023804 (2016)  ...  Our model is based on the electron quantum paths, a discrete number of electron trajectories, and continuum-bound transitions.  ...  Figure B: For the higher-order harmonics where there are no experimental data, we use a reference to a Schrodinger solver (Qprop) [3]. Fig A.  ... 
doi:10.1103/physreva.94.023804 fatcat:72zgb7qhkbdq7mdz2nhp7ofl5e

Fast Convergent Schrödinger-Poisson Solver for the Static and Dynamic Analysis of Carbon Nanotube Field Effect Transistors [chapter]

Mahdi Pourfath, Hans Kosina
2006 Lecture Notes in Computer Science  
In order to account for the ballistic transport we solved the coupled Poisson and Schrödinger equations for the analysis of these devices.  ...  In this work we show that this problem is due to inappropriate energy discretization, and by using an adaptive integration method the simulation time is reduced and most of the simulations converge in  ...  Acknowledgments This work was partly supported by the European Commission, contract No. 506844 (NoE SINANO), and the National Program for Tera-level Nano-devices of the Korea Ministry of Science and Technology  ... 
doi:10.1007/11666806_66 fatcat:jku22y34qrdazcjd2ky444fbfy

The Gaussian Wave Packet Transform for the Semi-Classical Schrödinger Equation with Vector Potentials

Zhennan Zhou and Giovanni Russo
2019 Communications in Computational Physics  
The numerical methods are proved to be unconditionally stable, spectrally accurate in space and second order accurate in time, and in principle they can be extended to higher order schemes in time.  ...  With this approach, the highly oscillatory Schrödinger equation is equivalently transformed into another Schrödinger type wave equation, the w equation, which is essentially not oscillatory and thus requires  ...  Appendices A Review of the Gaussian wave packet method In this part, we present a brief summary of the Gaussian beam method for the semiclassical Schrödinger equation with vector potentials (see [56]  ... 
doi:10.4208/cicp.oa-2018-0131 fatcat:4zn2kfzlzfbojmdxjlpvz5sgke

A fast and robust computational method for the ionization cross sections of the driven Schroedinger equation using an O(N) multigrid-based scheme [article]

Siegfried Cools, Wim Vanroose
2015 arXiv   pre-print
This paper improves the convergence and robustness of a multigrid-based solver for the cross sections of the driven Schroedinger equation.  ...  The proposed solver displays optimal scaling; a solution is found in a time that is linear in the number of unknowns.  ...  Acknowledgments This research is funded by the Research Council of the University of Antwerp. The authors additionally thank Bram Reps for fruitful discussions on the subject.  ... 
arXiv:1412.1953v4 fatcat:hmoreznqcjdibiim5qt3wbodei

AxioNyx: Simulating Mixed Fuzzy and Cold Dark Matter [article]

Bodo Schwabe, Mateja Gosenca, Christoph Behrens, Jens C. Niemeyer, Richard Easther
2020 arXiv   pre-print
Fuzzy (or ultralight, or axion-like) dark matter dynamics are governed by the comoving Schr\"odinger-Poisson equation.  ...  We find that the effective granule masses decrease in proportion to the fraction of fuzzy dark matter which quadratically suppresses soliton growth, and that a central soliton only forms if the fuzzy dark  ...  The finite differencing scheme uses a fourth order Runge-Kutta solver to evolve equations 1 and 2, and had previously been integrated with Nyx [39] .  ... 
arXiv:2007.08256v1 fatcat:wo6frezkzzbwpigd5x24hdohgu

Efficient Parallel Computing for Laser-Gas Quantum Interaction and Propagation

Emmanuel Lorin, André D. Bandrauk
2008 International Symposium on High-Performance Computing in an Advanced Collaborative Environment (HPCS'06)  
We present in this short paper some domain decomposition and high performance numerical techniques for simulating laser-gas interaction and propagation using a multiscale Maxwell-Schrödinger model.  ...  Ionization and high order harmonic generation are in particular taken into account in this micro-macro model, leading to additional simulation difficulties.  ...  In [4] , [5] we have introduced a multi-scale model coupling the macroscopic Maxwell equations modeling the propagation of an electro-magnetic field in a gas modeled by many Time Dependent Schrödinger  ... 
doi:10.1109/hpcs.2008.14 dblp:conf/hpcs/LorinB08 fatcat:dnpvfayzybdwdgrxyehygnjepu
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